Question

If \(A\) is any real number and \(r\) is positive rational number, then the value of \(\lim_{x \to +\infty} \frac{x^r}{e^{Ax}}\) is given by

• A. e
• B. -1
• C. 0
• D. 1

Hint:

Remember: \(e^{kx}\) grows faster than \(x^n\) for any finite \(n\) and \(k > 0\).
So \(\lim_{x \to \infty} \frac{x^n}{e^{kx}} = 0\).

Answer 1

The Correct Option is C